The present disclosure is related to thermoacoustic devices, and more specifically to a multiple-stage thermoacoustic device in which the stages are connected in series to provide improved power recovery and device efficiency.
The pulse-tube refrigerator, an example of which is shown in FIG. 1, typifies travelling-wave thermoacoustic refrigerators. In device 10, an acoustic wave travels through a gas. The pressure and velocity oscillations of the gas are largely in-phase in certain regions of the device. Thus, these devices are generally referred to as traveling-wave devices. See, for example, U.S. patent application Ser. No. 12/533,839 and U.S. patent application Ser. No. 12/533,874, each of which being incorporated herein by reference.
In device 10, an acoustic source 12, generally an electromechanical transducer such as a moving piston, generates oscillating acoustic energy in a sealed enclosure 14 containing compressed gas. Combinations of noble gases, notably helium, are often used, though many gases, including air, can be utilized. The acoustic energy passes through a first heat exchanger, the “hot” heat exchanger 16, generally connected, for example via heat exchange fluid, to a heat reservoir at ambient temperature, a regenerative heat exchanger, or “regenerator” 18 (described below), and another heat exchanger, the “cold” heat exchanger 20, which is connected, for example via heat exchange fluid, to the thermal load which is to be cooled by the refrigerator. Usually, the cold heat exchanger is followed by another tube, called a “pulse tube,” 22 and a last ambient-temperature heat exchanger, the “ambient” heat exchanger 24, which serves to isolate the cold heat exchanger and thereby reduce parasitic heat loading of the refrigerator. The “hot” heat exchanger 16 and “ambient” heat exchanger 24 are often a the same temperature. After the “ambient” heat exchanger is an acoustic load 26, often an orifice in combination with inertances and compliances, which dissipates acoustic energy. Here, a “heat exchanger” is taken to mean a device which exchanges heat between a gas inside the thermoacoustic device and an outside fluid, such as a stream of air.
In steady state, a temperature gradient is established in the regenerator in the direction from the hot to the cold heat exchanger. Heat is ideally transferred nearly isothermally between the gas and the regenerator material, often metal or ceramic porous material or mesh. With traveling-wave acoustic phasing, the gas in the regenerator undergoes an approximate Stirling cycle. In this way, the maximum heat can be moved from the cold to the hot heat exchanger per acoustic energy consumed.
Oscillating acoustic power is described by an oscillating pressure, P, in combination with an oscillating volume velocity, U, which is linear velocity, v, times the cross-sectional area of the enclosure. These quantities can be generally represented as complex phasors, P(t)=pejφPejωt and U(t)=uejφuejωt, with j representing the square root of −1, p and u representing peak magnitude of the pressure and volume velocity, respectively, ω representing the radial frequency of oscillation, and φp and φu representing constant phase offsets of the pressure and volume velocity components, respectively. The pressure is given by Pm+Re[P(t)], where Pm is the mean pressure. Likewise, the (signed) volume velocity is given by Re[U(t)]. The acoustic power is said to have travelling-wave phasing if P(t) and U(t) are in-phase, that is φP−φU=0. With travelling-wave phasing, the acoustic power is maximized for a given p and u.
A travelling-wave thermoacoustic refrigerator is characterized by the acoustic power having approximately travelling-wave phasing in the region of the regenerator. (In practice, it is impossible to have exactly travelling-wave phasing in the entire regenerator section.) With this phasing, the regenerator can be designed to approach optimal effectiveness, such that, ideally, the acoustic coefficient of performance (COP) of the refrigerator, which is given by
            COP      aco        =                            Q          .                C                                          E            .                    1                -                              E            .                    2                      ,can approach the thermodynamic optimum known as the Carnot limit
      COP    Car    =                    T        C                              T          H                -                  T          C                      .  . In the above formula, {dot over (Q)}c is the heat flux per unit time through the cold heat exchanger (i.e., the cooling power), Ė1 is the acoustic power incident on the regenerator, and Ė2 is the acoustic power leaving the regenerator. Ė2 has not been utilized for moving heat and remains available to do work.
For the phasing of the acoustic power in the region of the regenerator to be approximately travelling-wave, the acoustic load in a pulse-tube refrigerator must be dissipative. In other words, the power leaving the regenerator, Ė2, is discarded. The COP is therefore limited to
      COP    PTR    =                              Q          .                C                              E          .                1              .  As
                    E        .            2        ≈                  (                              T            C                                T            H                          )            ⁢                        E          .                1              ,if TC<<TH, as is the case for cryogenic cooling applications, Ė1−Ė2≈Ė1 and the reduction in COP is small. However, for smaller temperature changes, as are common for example in air conditioning and conventional refrigeration applications, Ė2 is relatively greater. In fact, as TC→TH, Ė2→Ė1. Therefore, discarding Ė2 greatly reduces the maximum efficiency.
One method of loss recovery has been proposed in the aforementioned U.S. patent application Ser. Nos. 12/533,839 and U.S. patent application Ser. No. 12/533,874. According to these disclosures, the “excess” acoustic power is converted to electrical power by a transducer. The electrical power produced by the transducer is combined with the base electrical power driving the acoustic source. However, the conversion process itself has inherent losses that reduce the overall efficiency of the loss recovery scheme.
Another method that has been proposed, for example by Swift et al., J. Acoust. Soc. Am. 105 (2), Pt 1, February 1999, pp 711-724 (which is incorporated herein by reference), to recover the lost power, Ė2, is by removing the acoustic load and coupling the end of the refrigerator to the back face of the source. An example of a device 30 according to this proposal is shown in FIG. 2. Device 30 includes an acoustic source 32 housed in a body 34. Also housed in body 34 are first heat exchanger 36, regenerator 38, and second heat exchanger 40. Optionally, device 30 may include a pulse tube 42 and/or a third heat exchanger 44 (in each of the embodiments described herein, the pulse-tube is optional as well as the third heat exchanger). Acoustic power exiting either second heat exchanger 40, or third heat exchanger 44 if present, is coupled to the backside of acoustic source 32 by way of an acoustic transmission line 46 (which in one embodiment is a channel through which an acoustic wave may travel). In this configuration, Ė3=αĖ2 is the portion of power Ė2 that is delivered to the back face of the source 32. The coefficient α represents losses in transmission line 46. The total power that must be generated by source 32 is thus Ė1−Ė3=Ė1−αĖ2 and the maximum COP is
      COP    1    =                              Q          .                C                                          E            .                    1                -                  α          ⁢                                    E              .                        2                                .  In devices of this type, transmission line 46 is necessarily long and lossy, so α is small and power recovery is not very effective.
In a looped thermoacoustic refrigerator of the type shown in FIG. 2, consider θP=arg(P1(t))−arg(P3(t)), the phase change of the oscillating pressure across the electromechanical transducer, or acoustic power generator. For positive power flow (arrows shown in FIG. 2), the phase angles between P1(t) and U1(t) and between P3(t) and U1(t) must both be less than 90°. Therefore 0°≦θP≦180°. The pressure phase change through the transmission line will approximate θT=θL−θP−θR, where θL represents the pressure phase change around the full loop and θR represents the pressure phase change in the regenerator and other functional parts of the refrigerator. For continuity, the pressure phase change around the full loop, θL, must be a multiple of 360°. As no benefit is derived from using a greater multiple, we can assume θL=360°. In an acoustic transmission line, the pressure and velocity phases both increase in the direction of power flow, giving θT>0°. Furthermore, in an effective travelling wave regenerator, the pressure phase change is always positive, and in practice, 0°<θR<90°. The non-negativity of θR and θP implies 0°<θT<θT. Consequently, θT=360°−θP−θR, and usually the transmission line phase change θT>180°. Such a large phase change requires a long, necessarily lossy, transmission line. The angle θT can in general be reduced by increasing θP, but this is at the cost of available power. Likewise, increasing θR will increase losses.
Where “excess” acoustic power (not consumed in the cooling cycle) moving away from the acoustic source is looped back through an acoustic transmission line to the backside of the acoustic source, losses in the transmission line can substantially diminish or even outweigh the gains from the power recovery. In yet another method of power recovery, the “excess” acoustic power is routed to the front face of the acoustic source. This method may suffer from losses due to mass streaming effects. Thus, methods of recovering the acoustic power and reducing loss have not sufficiently optimized power recovery.
In a thermoacoustic refrigerator, optimal efficiency is achieved if the electrical power that must be delivered to the acoustic source or sources is minimized for a given cooling power. On the other hand, the cooling power is maximized in part by maximizing the acoustic power incident on the part of the device containing the heat exchangers and regenerator with the phasing of said acoustic power being approximately traveling-wave in that part of the device. Some of the acoustic power is necessarily not used to move heat. For high efficiency, a large part of this “excess” acoustic power must be utilized to reduce the electrical power required by the acoustic source. Heretofore, it has not been possible to utilize a significant portion of this excess acoustic power.